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+1 vote
11.2k views
in Mathematics by (15.7k points)

Let A = {n ∈ N | n2 ≤ n + 10,000}, B = {3k +1 | k ∈ N} and C = {2k | k ∈ N}, then the sum of all the elements of the set A ∩ (B – C) is equal to_______ .

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1 Answer

+2 votes
by (15.2k points)

 B – C ≡ {7,13,19,...97, ....} 

Now, n2 – n ≤ 100 × 100 ≤ n(n – 1) ≤ 100 × 100 

\(\Rightarrow\) A = {1,2,...., 100}. 

So, A ∩ (B - C) = {7,13,19,...,97} 

Hence, sum = \(\frac{16}{2}\) (7 + 97) = 832

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